The exponentiated half logistic skew-t distribution with GARCH-type volatility models

Abstract

Most financial time series have non-normal features such as heavy tails, excess kurtosis and skewness. Financial asset returns volatility is also a significant measure in financial decisions, option pricing, risk management, and portfolio selection, so it is important to create vigorous driven conditional innovation density for GARCH-type volatility models for investigating volatility in financial time series. In this research, a new exponentiated half logistic skew-t (EHLST) innovation distribution for fitting generalized autoregressive conditional heteroskedasticity (GARCH)-type models is proposed. Structural properties of the proposed distribution such as density and distribution functions, quantile function and raw moments were derived. The maximum likelihood estimation criterion discussed is to estimate the parameters of the proposed distribution via a simulation study and real-life dataset. Application on Bitcoin digital-currency price index log-returns was carried-out to inspect the performance of the GARCH-type models with EHLST innovation density relative to five innovation densities in volatility modeling. The research results showed that the GARCH-EHLST model was selected as the best for the BTC log-returns conditional variance. More so, three forecasts performance measures were used to compare the out-of-sample performance of the models, and the GARCH-EHLST model outperformed the other models in terms of superior volatility predictive capability.

Keywords

• Bitcoin
• GARCH volatility model
• Maximum likelihood
• Skew-t distribution
• Simulation